The function f(x+y) = f(x)f(y) is known as a Cauchy functional equation.

Given that f(1) = a, we can find the value of f(50) by using the property of the function repeatedly.

Step 1: We know that f(1) = a.

Step 2: We can express 50 as 1+1+1+...+1 (50 times).

Step 3: Using the property f(x+y) = f(x)f(y), we can write f(50) as f(1+1+...+1) = f(1)f(1)...f(1) (50 times) = a*a*a*...*a (50 times) = a^50.

So, the value of f(50) is a^50.

Question

The function f(x+y) = f(x)f(y) is known as a Cauchy functional equation.

Given that f(1) = a, we can find the value of f(50) by using the property of the function repeatedly.

Step 1: We know that f(1) = a.

Step 2: We can express 50 as 1+1+1+...+1 (50 times).

Step 3: Using the property f(x+y) = f(x)f(y), we can write f(50) as f(1+1+...+1) = f(1)f(1)...f(1) (50 times) = a*a*a*...*a (50 times) = a^50.

So, the value of f(50) is a^50.

Knowee AI · Accepted Answer

The function f(x+y) = f(x)f(y) is known as a Cauchy functional equation.

Given that f(1) = a, we can find the value of f(50) by using the property of the function repeatedly.

Step 1: We know that f(1) = a.

Step 2: We can express 50 as 1+1+1+...+1 (50 times).

Step 3: Using the property f(x+y) = f(x)f(y), we can write f(50) as f(1+1+...+1) = f(1)f(1)...f(1) (50 times) = a*a*a*...*a (50 times) = a^50.

So, the value of f(50) is a^50.

f be a real function such that f(x+y) =f(x)f(y). If f(1) = a, what is the valueof f(50) ?